Complex diseases are generally caused by the dysregulation of biological functions rather than individual molecules. Hence, a major challenge of the systematical study on complex diseases is how to capture the differentially regulated biological functions, e.g., pathways. The traditional differential expression analysis (DEA) usually considers the changed expression values of genes rather than functions. Meanwhile, the conventional function-based analysis (e.g., PEA: pathway enrichment analysis) mainly considers the varying activation of functions but disregards the structure change of genetic elements of functions. To achieve precision medicine against complex diseases, it is necessary to distinguish both the changes of functions and their elements from heterogeneous dysregulated pathways during the disease development and progression. In this work, in contrast to the traditional DEA, we developed a new computational framework, namely differential function analysis (DFA), to identify the changes of element-structure and expression-activation of biological functions, based on comparative non-negative matrix factorization (cNMF). To validate the effectiveness of our method, we tested DFA on various datasets, which shows that DFA is able to effectively recover the differential element-structure and differential activation-score of pre-set functional groups. In particular, the analysis of DFA on human gastric cancer dataset, not only capture the changed network-structure of pathways associated with gastric cancer, but also detect the differential activations of these pathways (i.e., significantly discriminating normal samples and disease samples), which is more effective than the state-of-the-art methods, such as GSVA and Pathifier. Totally, DFA is a general framework to capture the systematical changes of genes, networks and functions of complex diseases, which not only provides the new insight on the simultaneous alterations of pathway genes and pathway activations, but also opens a new way for the network-based functional analysis on heterogeneous diseases.